The series ∑n=0∞rn\sum_{n=0}^{\infty} r^n∑n=0∞rn converges to 11−r\frac{1}{1-r}1−r1 if:
∣r∣<1|r| < 1∣r∣<1
∣r∣>1|r| > 1∣r∣>1
r=1r = 1r=1
r=−1r = -1r=−1